The timeless and placeless setting of "The Lottery" is meant to make it a universal story, one that could happen at any time and in any place. The author intends for us to be able to see the story as one that could happen in our own communities, to our own families, to us. She refers back to olden days to show us that this tradition has been going on for a very long time, for so long that its meaning is lost, but this is really the only reference one gets to any time period at all in the story. The point of wanting to make this story universal, one that could be read by any reader as meaningful, is to make a reader think about how foolish it is to blindly follow a tradition, a tradition that has no meaning, and how easily people can be led into being horrible to one another. Jackson reportedly stated that the Holocaust was on her mind when she wrote the story, an instance in which people, steeped in the "tradition" of Antisemitism, blindly followed their leader, which led to the senseless slaughter of six million Jews and countless others as well, for equally meaningless purposes. She is telling us that such things can happen in any time and any place.
The details are omitted because Jackson wants the reader to think it could happen at any time or any place. She did however add enough details to allow the reader to engulf his or herself to the setting and characters. Adding names and specific details makes the ending that much more unthinkable and memorable. She brilliantly enables us to place ourselves in the position of following a horrific tradition because everyone else does. This brings to mind many odd customs and traditions our society find acceptable.